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The Quarterly Journal of Mechanics and Applied Mathematics 1986 39(1):111-124; doi:10.1093/qjmam/39.1.111
© 1986 by Oxford University Press
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ENERGY-MINIMAL FINITE DEFORMATIONS OF A SYMMETRICALLY LOADED ELASTIC SHEET

G. P. MACSITHIGH

( Department of Engineering Mechanics, University of Missouri-Rolla Rolla, Missouri 65401, U.S.A. )

We study the homogeneous finite deformations of a rectangular sheet of a Mooney–Rivlin material subjected to equal tensile dead loads. We prove the existence of (at least one) homogeneous equilibrium which minimizes the potential energy of the system, and we determine the class of homogeneous minimizers for each value of the applied tension. In the process, we identify a critical value of a material parameter (the ratio of the Mooney–Rivlin constants) at which the qualitative nature of the solution class undergoes a change.


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